Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 8x + 3$ and $ BC = 2x + 51$ Find $AC$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {8x + 3} = {2x + 51}$ Solve for $x$ $ 6x = 48$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 8({8}) + 3$ $ BC = 2({8}) + 51$ $ AB = 64 + 3$ $ BC = 16 + 51$ $ AB = 67$ $ BC = 67$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {67} + {67}$ $ AC = 134$